A composition of a student of mine:
As I don't usually pay attention to the fact that I breathe, so I have not been aware of the importance of my family: they are always there.

What he's supposed to write is something like "To me, my family has been like the air we breathe; I haven't been conscious of their importance because they are always there."

Does the usage of "As...so..." in his sentence make sense? Does it sound natural to you native speakers?
IT sounds ok but a little ambiguous when written. In speech you would make the meaning clear.

'...so I have also not been aware...' clarifies things.
I agree with Nona's comment that it would have to be a little looser in speech.

I would associate this formation ('as is X, so is Y') with extended similes in verse:

'As an unperfect actor on the stage,
Who with his fear is put besides his part,
Or some fierce thing replete with too much rage,
Whose strength's abundance weakens his own heart;
So I, for fear of trust, forget to say
The perfect ceremony of love's rite...' (Shakespeare, Sonnet ***)

'Family environment = air' seems a just comparison. But:

'I breathe' – I am the active party.
'Someone else is important to me' – I am the ?passive party.